Russian Mathematics

, Volume 61, Issue 4, pp 72–88 | Cite as

On distribution of Grubbs’ statistics in case of normal sample with outlier

  • L. K. Shiryaeva


We investigate one-sided Grubbs’ statistics for a normal sample. Those statistics are standardized maximum and standardized minimum, i.e., studentized extreme deviation statistics. We consider the case of the sample when there is one abnormal observation (outlier), unknown to what number according. The outlier differs from other observations in values of population mean and dispersion. We obtain recursive relationships for the marginal distribution function of one-sided Grubbs’ statistics. We find asymptotic formulas for marginal distribution functions. We obtain recursive relationships for the joint distribution function of one-sided Grubbs’ statistics and investigate its properties.


one-sided Grubbs’ statistics standardized minimum and maximum outlier normal distribution marginal distribution functions asymptotic decompositions joint distribution function power functions for Grubbs’ criteria 


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© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Samara State Economic UniversitySamaraRussia

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